The graph of a polynomial function continues down on the left and continues up on the right. Which of the following must be true about this polynomial function?
a The function is even, with a positive leading coefficient. b The function is odd, with a positive leading coefficient. c The function is even, with a negative leading coefficient. d The function is odd, with a negative leading coefficient.

The solution set of the equation is {0}

A. The values of the variable that make a denominator zero are [tex]x = 3[/tex] and [tex]x = -3[/tex]. This is because when [tex]x = 3[/tex] or [tex]x = -3[/tex], the denominator of the fraction [tex]x^2 - 9[/tex] becomes zero, causing the entire equation to become undefined.

B. To find the solution of the equation, we can first multiply both sides by the common denominator, [tex]x^2 - 9[/tex]:

[tex](5/x+3-3/x-3)(x^2-9) = (5x/x^2-9)(x^2-9)[/tex]

Simplifying and combining like terms, we get:

[tex]5x - 9 - 3x + 9 = 5x[/tex]

[tex]2x = 5x[/tex]

Subtracting [tex]5x[/tex] from both sides, we get:

[tex]-3x = 0[/tex]

Dividing by -3, we find that the solution of the equation is x = 0.

Therefore, the solution set of the equation is {0}.

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The area οf the shaded regiοn will be (area οf bigger rectangle - area οf white rectangle) 5x²+7x-26.

A rectangle is a type οf quadrilateral, which is a fοur-sided pοlygοn. A rectangle has the fοllοwing prοperties:

It has fοur straight sides, which are perpendicular tο each οther (at right angles).

It has fοur right angles (90-degree angles).

Its οppοsite sides are equal in length and parallel tο each οther.

Its diagοnals are equal in length and bisect each οther.

Nοw,

Area οf shaded regiοn= area οf bigger rectangle - area οf white rectangle.

As Area οf rectangle= length × Breadth

then

Area of shaded region [tex]= (3x-4)(2x+2)-(x-3)(x-6)[/tex]

[tex]=6x^2+6x-8x-8 -x^2+6x+3x-18\\=5x^2+7x-26[/tex]

hence,

         The area οf the shaded regiοn will be 5x²+7x-26.

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Answer:

1/9

Step-by-step explanation:

I plugged it into a calculator.

Answer: Less than three would be like 2 or 1 or any negative number.

Step-by-step explanation: Three munis anything is less than the 3 you had to start with.

Step-by-step explanation:

The first step is to add 6 to both sides

3x =15+6

3x=21

Divide both sides by 3

X = 7

Answer:

16 percent decrease

Step-by-step explanation:

25. The scale factor is 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 115 degrees

25. The scale factor of JKLM and EFGH is calculated using corresponding sides

side EF * scale factor = side JK

8 * scale factor = 20

scale factor = 20 / 8

scale factor = 2.5

26. The congruent angles include

∠ E = ∠ J = 65 degrees

∠ F = ∠ K = 90 degrees

∠ G =  L = 90 degrees

∠ H = ∠ M = 360 - 90 - 90 - 65 = 115 degrees

27.  the ratios of the corresponding side lengths

JK / EF is proportional to KL / FG is proportional to LM / GH is proportional to MJ / EH

28. the values of x, y, and z

x = 2.5 * FG = 2.5 * 11 = 27.5

y = 30 / 2.5 = 12

z = 65 degrees

29. the perimeter of each polygon

the smaller polygon EFGH = 8 + 11 + 3 + 12 = 34

the bigger polygon JKLM = 20 + 27.5 + (3 * 2.5) + 30 = 85

30. the ratio of the perimeters of JKLM to EFGH

= 85 / 34 = 2.5

31. the area of each polygon

the smaller polygon EFGH = 0.5(3 + 8) * 11 = 60.5

the bigger polygon JKLM = 0.5(20 + 7.5) * 27.5 = 378.125

32. the ratio of the areas of JKLM to EFGH​

= 378.125 / 60.5 = 6.25

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Answer:

11.97 lb

Step-by-step explanation:

To find the force that the rope must exert on the cart to keep it from rolling down the ramp, we need to resolve the forces acting on the cart along the direction of the ramp and perpendicular to the ramp.

First, we resolve the weight of the cart into its components. The weight of the cart acting vertically downwards can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

W_perp = W * cos(theta) = 40lb * cos(15°) = 38.6lb

The component parallel to the ramp is given by:

W_parallel = W * sin(theta) = 40lb * sin(15°) = 10.4lb

where W is the weight of the cart, and theta is the angle of inclination of the ramp.

Next, we resolve the force exerted by the rope into its components. The force exerted by the rope can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

F_perp = F * cos(phi) = F * cos(60°) = 0.5F

The component parallel to the ramp is given by:

F_parallel = F * sin(phi) = F * sin(60°) = 0.87F

where F is the force exerted by the rope, and phi is the angle of inclination of the rope.

To keep the cart from rolling down the ramp, the force exerted by the rope must balance the weight of the cart along the direction of the ramp. That is,

F_parallel = W_parallel

0.87F = 10.4lb

Solving for F, we get:

F = 11.97lb

Therefore, the force that the rope must exert on the cart to keep it from rolling down the ramp is approximately 11.97lb.

The greatest common factor of 8m2 and 7b3 is the largest monomial that can divide both 8m2 and 7b3. So, the greatest common factor of 8m^(2) and 7b^(3) is 1.


The greatest common factor (GCF) of two monomials is the product of the greatest common factor of their coefficients and the greatest common factor of their variables. In this case, the greatest common factor of the coefficients is 1, since 8 and 7 have no common factors other than 1. The GCF of the variables is 1, since m and b have no common factors. Therefore, the GCF of 8m^(2) and 7b^(3) is 1*1 = 1.

Here is a step-by-step explanation:
1. Find the GCF of the coefficients: GCF(8,7) = 1
2. Find the GCF of the variables: GCF(m^(2),b^(3)) = 1
3. Multiply the GCF of the coefficients and the GCF of the variables: 1*1 = 1
4. The GCF of 8m^(2) and 7b^(3) is 1.

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What is rhombus ?

A rhombus is a special type of parallelogram in which two pairs of opposite sides are congruent. That means all the sides of a rhombus are equal.

What is the Area of a Rhombus?

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. To recall, a rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

Using Diagonals                A = ½ × d1 × d2

Using Base and Height        A = b × h

Using Trigonometry        A = b2 × Sin(a)

the correct answer is the option (C) 340 cm^2

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Answer:

isosceles triangle.

Step-by-step explanation:

To classify triangle WXY by its sides, we need to determine whether all three sides are equal, two sides are equal, or all three sides are different. We can do this by calculating the lengths of the sides using the distance formula:

Side WX:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(-1 - 4)^2 + (-3 - (-10))^2] = sqrt[5^2 + 7^2] = sqrt(74)

Side WY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - 4)^2 + (-5 - (-10))^2] = sqrt[7^2 + 5^2] = sqrt(74)

Side XY:

sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - (-1))^2 + (-5 - (-3))^2] = sqrt[12^2 + 2^2] = sqrt(148)

Since the lengths of sides WX and WY are equal, but the length of side XY is different, we can classify triangle WXY as an isosceles triangle. Specifically, it is an isosceles triangle with sides WX and WY equal.

Therefore , the solution of the given problem of percentage comes out to be 38 years old is the median age.

In statistics, a "a%" is a figure or statistic that is expressed as a percentage of 100. The words "pct," "pct," but instead "pc" are also not frequently used. However, the sign "%" is frequently used to represent it. The percentage sum is flat; there are no dimensions. Percentages are truly integers because their numerator almost always equals 100. Either the % symbol (%) or the additional term "fraction" must come before a number to denote that it is a percentage.

Here,

The following algorithm must be used to determine the mean age:

=> mean = (all years added together) / (total number of persons)

The representative age for each age group is the age that falls in the middle of the range. With this approach, we can determine the total age as follows:

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

=> 162 + 644 + 924 + 2970 + 4636 + 2688 + 1152 + 1520 + 272.25

=>18(9) + 23(28) + 28(33) + 33(90) + 38(122) + 56(48) + 48(24) + 76(20) + 1089(0.25)

According to the information provided, there are 460 people in total.

=> mean = 17745.25 / 460

=> mean = 17745.25 / 460

As a result, the average lifespan is roughly 38.552 years.

The age category in this instance with the highest frequency has a midpoint of 38 and a frequency of 122. As a result, 38 years old is the median age.

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Answer: If you did 100 Joules of work to lift your backpack, then the work you did is equal to the force applied multiplied by the distance lifted. Let's say you lifted the backpack a distance of d meters with a force of F Newtons. Then:

100 J = F x d

Now, if half of everything falls out of your backpack, the force required to lift the backpack will be reduced by half, so the new force required will be F/2. The distance lifted remains the same. So the work done to lift the backpack using half the force is:

Work = (Force x Distance) / 2

= (F x d) / 2

But we know that F x d = 100 J, so we can substitute this in the equation above:

Work = (F x d) / 2

= 100 J / 2

= 50 J

Therefore, the work you will do to lift your backpack the same distance with half the force is 50 Joules.

Step-by-step explanation:

Answer:

-----------------------

As per table we see:

Since the difference of both variables is common, the function is linear.

The matching choice is C.

We can see here that the experimental probability that it will snow in March is:

Experimental probability is the probability that an event will occur based on actual experiments or observations.

It is calculated by performing an experiment or conducting observations, counting the number of times the event of interest occurs, and dividing that count by the total number of trials or observations.

Mathematically, the formula for the experimental probability is defined by:

Probability of an Event P(E) = Number of times an event occurs / Total number of trials.

Number of times it snowed = 2

Total number of trials = 5.

Thus, the experimental probability will be: 2/5.

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The expression is not a polynomial, as it's exponent is not an integer number.

An expression represents a polynomial when these following conditions are satisfied:

The exponent for this problem is of [tex]5\sqrt{7}[/tex], which is a non-integer exponent, hence the expression is not a polynomial. Any integer exponent would make the expression in fact represent a polyonomial.

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According to the solving  the value of given function h’(5) h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input.

To find the value of h’(5), we need to find the derivative of h(x) first. We can use the product rule and the quotient rule to do that:

h(x) = f(x)g(x) + f(x)/g(x)

h’(x) = f’(x)g(x) + f(x)g’(x) + [g(x)f’(x) – f(x)g’(x)] / g(x)² (by the quotient rule)

h’(x) = [f’(x)g(x) + g(x)f’(x)] / g(x)² + [f(x)g’(x) – f(x)g’(x)] / g(x)² + f(x) / g(x)²

h’(x) = [2f’(x)g(x)] / g(x)² + f(x) / g(x)²

Now we can find h’(5) by plugging in x = 5:

h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

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angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

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The distance between the x and y intercepts of that line is √13/2. The correct answer is (B).

To find the distance between the x and y intercepts of a line, we can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)

First, we need to find the x and y intercepts of the line. The x intercept is where the line crosses the x-axis, so we can set y to 0 and solve for x. Similarly, the y intercept is where the line crosses the y-axis, so we can set x to 0 and solve for y.

Using the point-slope form of a line, we can find the equation of the line passing through the points (1,2) and (−0.5,1):
y - 1 = (1 - 2)/(−0.5 - 1)(x - (-0.5))
y - 1 = -2(x + 0.5)
y = -2x - 1

Now we can find the x and y intercepts:
For the x intercept, set y to 0:
0 = -2x - 1
2x = -1
x = -1/2

For the y intercept, set x to 0:
y = -2(0) - 1
y = -1

So the x intercept is (-1/2, 0) and the y intercept is (0, -1). Now we can use the distance formula to find the distance between these two points:
d = √((-1/2 - 0)² + (0 - (-1))²)
d = √((-1/2)² + (1)²)
d = √(1/4 + 1)
d = √(5/4)
d = √13/2

Therefore, the distance between the x and y intercepts of the line is √13/2.

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Answer: -sqrt(3)/4

Step-by-step explanation:

To solve this trigonometric expression, we can use the following trigonometric identities:

sin (180 + x) = -sin x

cos (180 + x) = -cos x

Using these identities, we can rewrite the expression as:

sin(200°)cos(80°) - cos(200°)sin(80°)

= sin(180° + 20°)cos(80°) - cos(180° + 20°)sin(80°)

= -sin(20°)cos(80°) + cos(20°)sin(80°)

= (cos(20°) - sin(20°))sin(80°)

= sin(70°)sin(80°)

= (cos(20°) - cos(150°))/2

= (-sqrt(3)/2 - sqrt(3)/2)/2

= -sqrt(3)/4

Therefore, sin(200°)cos(80°) - cos(200°)sin(80°) = -sqrt(3)/4.

Answer:

x = 50

Step-by-step explanation:

sin 40º = 32 / x

0.64 = 32 / x

x = 32 / 0.64

x =~ 50

The graph is shown in the image attached.

To solve an equation by graphing, you need to graph the equation on a coordinate plane and find the points where the graph intersects the x-axis. These points correspond to the solutions of the equation, which are the values of x that make the equation true here.

Therefore, to solve the equation by graphing, we plot the graph, locate the points where the graph intersects the x-axis, and read the solutions from the graph.

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ZW = 5.656

Since XY ≅ XZ ≅ YZ, △XYZ is an equilateral triangle. This means △XYZ is also equiangular.

Find the measures of the following angles in degrees:

m∠WYZ = 60°

m∠YWZ = 60°

m∠YZW = 60°

Find WY:

WY = 8

Find ZW: Give your answer in both simplest radical form and as an approximation correct to two decimal places.

simplest radical form ZW = 4√2

approximation ZW = 5.656854249492381

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a)1.746

b)0.119

To compare the null hypothesis that the population mean of the increase in sales is at least 50 units against the observed mean of 41.3 units, we will use both the critical value approach and the p-value approach.

For the critical value approach, we need to use the standard deviation of 12.2 units as well as the sample size of 20 supermarkets. This gives us a critical value of 1.746. As the observed mean (41.3 units) is less than 1.746 standard deviations away from the mean of 50 units, we can conclude that the null hypothesis cannot be rejected at the 5% level of significance.

For the p-value approach, we will use the same sample size and standard deviation. This gives us a p-value of 0.119, which is greater than the 5% level of significance. Thus, we can also conclude that the null hypothesis cannot be rejected at the 5% level of significance.

It is important to note that we are assuming that the data is normally distributed, and that there is no bias in the sample.

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The expression when evaluated is 256

From the question, we have the following parameters that can be used in our computation:

8 power of 8/3

Mathematically, this can be expressed as

8^(8/3)

When evaluated using a calculator, we have

8^(8/3) = 256

Hence, the solution is 256

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The given equation is z = 1 + iβ/β + 2i. We need to determine the value(s) for β such that the equation holds true.

First, we can multiply both sides of the equation by β + 2i to get rid of the denominator:

z(β + 2i) = 1 + iβ

Next, we can distribute the z on the left-hand side of the equation:

zβ + 2iz = 1 + iβ

Now we can rearrange the equation to get all the β terms on one side:

zβ - iβ = 1 - 2iz

We can factor out the β on the left-hand side:

β(z - i) = 1 - 2iz

Finally, we can divide both sides of the equation by z - i to get the value of β:

β = (1 - 2iz)/(z - i)

This is the value of β that satisfies the given equation. None of the given options match this value, so the correct answer is "None of the given options."

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1/4

The nth term of a geometric sequence can be found using the formula:

a_(n) = a_(1) * r^(n-1)

where a_(1) is the first term of the sequence and r is the common ratio.

Given a_(1) = 4, r = 1/2, and n = 5, we can substitute these values into the formula to get:

a_(5) = 4 * (1/2)^(5-1)

= 4 * (1/2)^4

= 4 * (1/16)

= 1/4

Therefore, the 5th term of the geometric sequence is a_(5) = 1/4.

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The number line is plotted on the graph below

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the number line be represented by graph A

Now , the points on the graph are

A = { 4 , -3 , 1 }

The opposites of the number points A is given by

A' = { -4 , 3 , -1 }

The values of the sets A and A' are plotted on the line plot graph

Hence , the line plot is solved

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It will take about 5.18 years for the car to be worth 8,200.

We can use the given formula to find the value of the car after x years:

[tex]V = 20,000(0.8)^x[/tex]

We want to know how long it will take for the car to be worth 8,200. So we can set V equal to 8,200 and solve for x:

[tex]8,200 = 20,000(0.8)^x[/tex]

Dividing both sides by 20,000 gives:

[tex]0.41 = (0.8)^x[/tex]

Taking the logarithm of both sides with base 0.8, we get:

[tex]log0.8(0.41) = x[/tex]

Using a calculator, we can find:

x ≈ 5.18

Therefore, it will take about 5.18 years for the car to be worth 8,200.

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